The Manchester City striker had gone quiet for long spells at MetLife Stadium before breaking the deadlock with a header in the 79th minute, converting Andreas Schjelderup's cross to put Stale Solbakken's side ahead.
He then settled the contest with a thumping left-footed strike from the edge of the box in the 90th minute, leaving Brazil needing something special to salvage the tie.
Neymar, introduced as a substitute earlier in the match, did pull one back from the penalty spot deep into stoppage time after Leo Ostigard caught Casemiro with an elbow, but it proved to be nothing more than a consolation in what is likely to have been the veteran's final World Cup appearance.
The result ends a difficult tournament for Brazil under Carlo Ancelotti, extending their run without reaching a quarter-final via a straightforward path against European opposition, and sends Norway through to face either Mexico or England in Miami next weekend.
Speaking after the match, Norway head coach Stale Solbakken said the performance was one the whole nation could be proud of.
"I think everyone who's a Norwegian citizen can enjoy this evening. That was a real thriller - it could have gone either way. But we played a solid, tactical game. We had a few turnovers that could have cost us. But all in all, it went our way, and we should be damn proud of that," Solbakken said.
The Norway coach also explained the tactical approach that helped his side overcome one of the tournament favourites.
"Why did it go our way? Well, we're playing - it's a bit like Manchester City versus Real Madrid. They sit back and rely on counterattacks, and we have to wear them down. Because that's what we're best at, and I think we did a good job of it," he said.
Haaland, who now sits level with Kylian Mbappe and Lionel Messi at the top of the Golden Boot standings on seven goals, reflected on his knack for finding the net in crucial moments.
"That's just how it usually goes. If I get a chance or two, it usually ends up as a goal. I don't know how I do it, but that's how I do it, so it's all about staying focused. I tell myself the chance will come, and then I usually know right away if I don't score," Haaland said.
"I'm starting to realise now, I think, that it's a gift from God that it goes in perfectly, perfectly right up against the post and stuff. So it's crazy."
The striker also spoke about what victory meant to him personally and for Norway as a nation.
"We just kept pushing forward, but I hope that all the young people watching this interview - I hope that when you get a little older, you'll see playing for Norway as the proudest thing you'll ever do in your entire life - it's absolutely insane," Haaland said.
Norway, appearing at their first World Cup since 1998, will now turn their attention to the quarter-final draw as they continue an historic run in the competition.